{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JOPLXNAH7GO54QNHH5LQDDXZ5Z","short_pith_number":"pith:JOPLXNAH","canonical_record":{"source":{"id":"1308.4645","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-21T17:53:24Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"title_canon_sha256":"a3e7846ff5a646b2f3b16f4b3d0fc6004556dc3fcb317be0937923ab58b98f1f","abstract_canon_sha256":"865185109e58b4b3b155abf0c1f773ac4ff1ec52b82223aa0dbeda1f9e5ed20d"},"schema_version":"1.0"},"canonical_sha256":"4b9ebbb407f99dde41a73f57018ef9ee487eebdf9d35f7697194d30e1a418f5d","source":{"kind":"arxiv","id":"1308.4645","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4645","created_at":"2026-05-18T03:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4645v3","created_at":"2026-05-18T03:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4645","created_at":"2026-05-18T03:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"JOPLXNAH7GO5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JOPLXNAH7GO54QNH","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JOPLXNAH","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JOPLXNAH7GO54QNHH5LQDDXZ5Z","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4645","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-21T17:53:24Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"title_canon_sha256":"a3e7846ff5a646b2f3b16f4b3d0fc6004556dc3fcb317be0937923ab58b98f1f","abstract_canon_sha256":"865185109e58b4b3b155abf0c1f773ac4ff1ec52b82223aa0dbeda1f9e5ed20d"},"schema_version":"1.0"},"canonical_sha256":"4b9ebbb407f99dde41a73f57018ef9ee487eebdf9d35f7697194d30e1a418f5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:44.343340Z","signature_b64":"g7EUBQUmvYsUsKSgVGVGrIN3jc8hzToprFlSBfKbCmAlrTjklsUh/9l5Vrkjr0+L8WI3ZRZanZt9SesyrrCYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b9ebbb407f99dde41a73f57018ef9ee487eebdf9d35f7697194d30e1a418f5d","last_reissued_at":"2026-05-18T03:06:44.342918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:44.342918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4645","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hR/RgAFOJ6D1hnq8gk3c37dZOKCQnIbQFBoHKTKe9Vrkisys68eLqg+5UL5c4a5beZBVa+odEV2YyiytLxbeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:35:20.153970Z"},"content_sha256":"79461f411313872a6b1e0c938cd9756f882377edce640a75005487b26b4860f3","schema_version":"1.0","event_id":"sha256:79461f411313872a6b1e0c938cd9756f882377edce640a75005487b26b4860f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JOPLXNAH7GO54QNHH5LQDDXZ5Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the completeness of solutions of Bethe's equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Andrew J. Sommese, Rafael I. Nepomechie, Wenrui Hao","submitted_at":"2013-08-21T17:53:24Z","abstract_excerpt":"We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of numbers of so-called singular (or exceptional) solutions. Using homotopy continuation methods, we find all such solutions of the Bethe equations for chains of length up to 14. The numbers of these solutions are in perfect agreement with the conjecture. We also discuss an indirect method of finding solutions of the Bethe equations by solving the Baxter T-Q equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4645","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f97bOzLLSjaBFM45jNfOI3evpQD57IzKWxWgWr5fniUl750S1VkPoIaN/BJNdIGJS4FaULDVxGCqdDuAv+v0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:35:20.154345Z"},"content_sha256":"d85aba284781881db1a15882ccba96c2638eb4f6112884f10e8e12afa594fda1","schema_version":"1.0","event_id":"sha256:d85aba284781881db1a15882ccba96c2638eb4f6112884f10e8e12afa594fda1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JOPLXNAH7GO54QNHH5LQDDXZ5Z/bundle.json","state_url":"https://pith.science/pith/JOPLXNAH7GO54QNHH5LQDDXZ5Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JOPLXNAH7GO54QNHH5LQDDXZ5Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T05:35:20Z","links":{"resolver":"https://pith.science/pith/JOPLXNAH7GO54QNHH5LQDDXZ5Z","bundle":"https://pith.science/pith/JOPLXNAH7GO54QNHH5LQDDXZ5Z/bundle.json","state":"https://pith.science/pith/JOPLXNAH7GO54QNHH5LQDDXZ5Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JOPLXNAH7GO54QNHH5LQDDXZ5Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JOPLXNAH7GO54QNHH5LQDDXZ5Z","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"865185109e58b4b3b155abf0c1f773ac4ff1ec52b82223aa0dbeda1f9e5ed20d","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-21T17:53:24Z","title_canon_sha256":"a3e7846ff5a646b2f3b16f4b3d0fc6004556dc3fcb317be0937923ab58b98f1f"},"schema_version":"1.0","source":{"id":"1308.4645","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4645","created_at":"2026-05-18T03:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4645v3","created_at":"2026-05-18T03:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4645","created_at":"2026-05-18T03:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"JOPLXNAH7GO5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JOPLXNAH7GO54QNH","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JOPLXNAH","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:d85aba284781881db1a15882ccba96c2638eb4f6112884f10e8e12afa594fda1","target":"graph","created_at":"2026-05-18T03:06:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of numbers of so-called singular (or exceptional) solutions. Using homotopy continuation methods, we find all such solutions of the Bethe equations for chains of length up to 14. The numbers of these solutions are in perfect agreement with the conjecture. We also discuss an indirect method of finding solutions of the Bethe equations by solving the Baxter T-Q equ","authors_text":"Andrew J. Sommese, Rafael I. Nepomechie, Wenrui Hao","cross_cats":["cond-mat.str-el","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-21T17:53:24Z","title":"On the completeness of solutions of Bethe's equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4645","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:79461f411313872a6b1e0c938cd9756f882377edce640a75005487b26b4860f3","target":"record","created_at":"2026-05-18T03:06:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"865185109e58b4b3b155abf0c1f773ac4ff1ec52b82223aa0dbeda1f9e5ed20d","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-21T17:53:24Z","title_canon_sha256":"a3e7846ff5a646b2f3b16f4b3d0fc6004556dc3fcb317be0937923ab58b98f1f"},"schema_version":"1.0","source":{"id":"1308.4645","kind":"arxiv","version":3}},"canonical_sha256":"4b9ebbb407f99dde41a73f57018ef9ee487eebdf9d35f7697194d30e1a418f5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b9ebbb407f99dde41a73f57018ef9ee487eebdf9d35f7697194d30e1a418f5d","first_computed_at":"2026-05-18T03:06:44.342918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:44.342918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g7EUBQUmvYsUsKSgVGVGrIN3jc8hzToprFlSBfKbCmAlrTjklsUh/9l5Vrkjr0+L8WI3ZRZanZt9SesyrrCYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:44.343340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4645","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79461f411313872a6b1e0c938cd9756f882377edce640a75005487b26b4860f3","sha256:d85aba284781881db1a15882ccba96c2638eb4f6112884f10e8e12afa594fda1"],"state_sha256":"5af82ddc8a195c003a244cb8baece88b9ed6c42e318b3d1e9b2fe4c19ead2f5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"28w0Wm8ZWr2G6MnsQoXBA3+LSNHpBG16YSF2LFyvX5N3A+JlpzXtUrDrXa36J4SoF8aBHAF5C+bhIE8KrKTCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:35:20.156222Z","bundle_sha256":"2809a0adee73a0d0939d808377b4f71ea8c42fd04afc687dbff07d7fe726e03b"}}